5.2 Search Techniques and Heuristics

Although summary information is valuable for finding conflict free or
coordinated plans at abstract levels, this information can also be
valuable in directing the search to avoid branches in the search space
that lead to inconsistent or suboptimal coordinated plans. A coordinator can prune away inconsistent
coordinated plans at the abstract level by doing a quick
check to see if is false.
For example,
if the search somehow reached the state shown in Figure
8b, the coordinator could backtrack before
expanding the hierarchies further and avoid reasoning about details of
the plans where they must fail.

Another strategy is to first expand plans involved in the most
threats. For the sake of completeness, the order of plan expansions
does not matter as long as they are all expanded at some point when
the search trail cannot be pruned. But, employing this ``expand on
most threats first'' (EMTF) heuristic aims at driving the search down
through the hierarchy to find the subplan(s) causing conflicts with
others so that they can be resolved more quickly. This is similar to
a most-constrained variable heuristic often employed in constraint
satisfaction problems. For example, if the facilities and inventory
managers wished to execute their plans concurrently as shown in Figure
17a, at the most abstract level, the coordinator would
find that there are conflicts over the use of transports for moving parts.
Instead of decomposing and reasoning about plan details
where there are no conflicts, the EMTF heuristic would choose to
decompose either or which have the most
conflicts. By decomposing the agents can resolve
the remaining conflicts and still execute concurrently.

Figure 17:EMTF heuristic resolving conflicts by decomposing
the plan

Another heuristic that a coordinator can use in parallel with EMTF
is ``choose fewest threats first'' (CFTF). Here the search orders states in
the search queue by ascending numbers of threats left to resolve. In
effect, this is a least-constraining value heuristic used in
constraint satisfaction approaches. As mentioned in Section
4.1, threats are identified by the
algorithm. By trying to resolve the threats of coordinated plan search
states with fewer conflicts, it is hoped that solutions can be found
more quickly. So, EMTF is a heuristic for ordering subplans to
expand, and CFTF, in effect, orders subplan choices.
For example, if the production manager chooses to use machine M1 instead of M2 to produce G, the coordinator is likely closer to a solution because there are fewer conflicts to resolve.
This heuristic can
be applied not only to selecting subplan choices but also to
choosing temporal constraints and variable bindings or any search operator
from the entire set of operators.

In addition, in trying to find optimal solutions in the style of a
branch-and-bound search, the coordinator can use the cost of abstract solutions to
prune away branches of the search space whose minimum cost is greater
than the maximum cost of the current best solution. This is the role
of the Dominates function in the description of the coordination
algorithm in Section 5.1. This usually assumes that
cost/utility information is decomposable over the hierarchy of
actions, or the cost of any abstract action is a function of
its decompositions.